Environmental Modelling: An Uncertain Future?

Keith Beven

Complex environmental models often handle uncertainty poorly — and when
they do provide uncertainty estimates decision-makers often ignore or
misuse them. In Environmental Modelling: An Uncertain Future? Keith
Beven offers a guide to uncertainty for both modelers and users of models.

Beven begins with a general introduction to the modeling process,
covering parameters, variables and boundary conditions, problems of
scale and incommensurability, model spaces and model ensembles, as well
as the uses of models in prediction and simulation. He argues for the
importance of dealing with uncertainty and surveys different kinds of
uncertainty and uncertainty estimation methods.

Chapter two is something of an epistemological and philosophical
digression. Beven argues for some kind of pragmatic realism, or a
"critical realism" following Bhaskar. He explores issues with model
validation, falsification, and Bayesian confirmation (evaluating
predictions against observations). He explains why adding explanatory
depth to a model is not always good (over-parameterisation). And he
suggests that though unexpected extreme events pose a challenge for models
they are also opportunities, since we learn the most when our models fail.

With simulations without historical data, "the results [of any
sensitivity or uncertainty analysis] will always be conditional on the
assumptions made". Independence is often assumed in practice, but we
may have to deal with covariation between parameters and variables.
Beven presents some ways of sampling model space (Monte Carlo, Latin
Hypercube, copula), doing sensitivity analysis, and using simplified
models for exploring parameter space and interpolating between results.
Where no probabilities can be assigned to uncertainties, the only option
may be to model multiple scenarios separately.

With historical data, there arises the "inverse problem" of estimating
model parameters. There may still be no "right" answer here, but
"we can use the data available to refine and hopefully constrain our
estimates of the uncertainty associated with any model predictions".
Statistical methods here include non-linear regression and formal
Bayesian methods. The latter seem an obvious choice, but they need a
formal likelihood measure and, with model structural errors that may
be inseparable from residual errors, can result in overconditioning;
they also lack the ability to reject models.

Alternative tools include fuzzy sets and what Beven calls Generalised
Likelihood Uncertainty Estimation (GLUE). The latter involves a (possibly
informal) likelihood measure for evaluating model runs, with criteria for
rejecting non-behavioural models outright, and the generation of random
realisations of models consistent with choices of parameter and input
variable distributions. With a formal measure this is equivalent to the
Bayesian approach, but Beven argues that there is a case for "common-sense
model evaluations and informal likelihood methods"; GLUE can help avoid
over-conditioning and has, over formal Bayesian methods, "the advantage
that the equifinality of models as hypotheses, non-stationarities in
the residual errors, and model failures are more clearly revealed".

When forecasting the near future, some kind of updating or data
assimilation is needed to allow new data to be used in updating model
predictions. One approach is to model the residual error, but it's also
possible to update the core model parameters. Certain lead times may
be critical, in which case it makes sense to minimise error variance
at those times. Beven explains the Kalman filter, the ensemble Kalman
filter, and a Monte Carlo method called Particle filtering, with examples
of their applications to flood models. He also looks at variational
(3DVar and 4DVar data assimilation) and ensemble methods in numerical
weather forecasting.

Decision making with uncertainty poses another set of problems.
Here Beven surveys tools and methods such as Bayesian Belief Networks,
Evidential Reasoning, decision support systems, and Info-Gap decision
theory (using concepts of robustness and opportuneness for dealing with
non-probabilistic uncertainties). One problem is evaluation of the
benefits of investment in additional information to reduce uncertainty.
And explaining uncertainty to diverse groups of stakeholders is a
practical challenge.

A final chapter touches on a mix of ideas. Unknowability and uncertainty
are not just the result of poor models. We need to accept an uncertain
future and approach modeling as a way of learning about places and
learning about model structures. The reluctance of decision-makers to
address uncertainty may lead to them passing responsibility onto modelers
— who in turn prefer to pass it on to their models.

The more mathematical material in Environmental Modelling is
segregated into twelve "boxes", which are basically appendices at
the end of chapters, taking up about a quarter of the text in total.
These range from basic material such as "Simple operations with
probability-distributed variables" to more advanced topics such as
"Kalman filter methods for data assimilation". Beven also provides some
information about software packages for particular applications.

Beven is a hydrologist and a majority of his examples are from flood and
groundwater models, while others are taken from climate science, ecology,
and fire management. (There's no attempt to compare the treatment of
uncertainty in environmental models with uncertainty in other domains,
say in finance.) Environmental Modelling will be useful for anyone
working with environmental models, though it's not a source of quick
answers for practical questions or solutions for specific problems.
It will also have an appeal to anyone who has to deal with scientific
uncertainty more generally.